运筹学英文上课录象

3IntroductiontoLinearProgramming3.1PrototypeExample3.2TheLinearProgrammingModel3.3AssumptionsofLinearProgramming3.4AdditionalExamples3.5SomeCaseStudies3.6ConclusionsInthislesson:Theteachingobjectsare:(1)Mastertheformulationoflinearprogrammingmodel(2)UnderstandtheprocedureofsolvinglinearprogrammingbyusingEXCELSOLVERTheteachingcontentsare:(1)PrototypeExample(2)Thebasicstepsofformulatingamodeloflinearprogramming(3)SolvingalinearprogrammingbyuseEXCELSOLVERThedevelopmentoflinearprogramminghasbeenrankedamongthemostimportantscientificadvancesofthemid-20thcentury,andwemustagreewiththisassessment.Itsimpactsincejust1950hasbeenextraordinary.Todayitisastandardtoolthathassavedmanythousandsormillionsofdollarsformostcompaniesorbusinessesofevenmoderatesizeinthevariousindustrializedcountriesoftheworld;anditsuseinothersectorsofsocietyhasbeenspreadingrapidly.Linearprogramminginvolvesthegeneralproblemofallocatinglimitedresourcesamongcompetingactivitiesinabestpossibleway.Itusesamathematicalmodeltodescribetheproblemofconcern.Andtheremarkablyefficientsolutionproceduretothelinearprogrammingiscalledthesimplexmethod.3.1PrototypeexampleTheWKYNDORGLASSCO.produceshigh-qualityglassproducts,includingwindowsandglassdoors.Ithasthreeplants.AluminumframesandhardwarearemadeinPlant1,woodframesaremadeinPlant2,andPlant3producestheglassandassemblestheproducts.Becauseofdecliningearnings,topmanagementhasdecidedtorevampthecompany’sproductline.Unprofitableproductsarebeingdiscontinued,releasingproductioncapacitytolaunchtwonewproductshavinglargesalespotential:Product1:an8-footglassdoorwithaluminumframingProduct2:A4*6footdouble-hungwood-famedwindowplantProductiontimeperbatch,hoursProductiontimeavailableperweek,hoursproduct1212310302241218Profitperbatch$3,000$5,000TheORteamgatherthefollowingproductiondata:Thequestionis:Determinewhattheproductionratesshouldbeforthetwoproductsinordertomaximizetheirtotalprofit,subjecttotherestrictionsimposedbythelimitedproductioncapacitiesavailableinthethreeplants.(Eachproductwillbeproducedinbatchesof20,sotheproductionrateisdefinedasthenumberofbatchesproducedperweek.)QuestionAnalysisplantProductiontimeperbatch,hoursProductiontimeavailableperweek,hoursproduct1212310302241218Profitperbatch$3,000$5,000Thedecisionvariableis:x1=?x2=?Theobjectiveismaximizetheprofit:2153maxxxzTheconstraintsare:Plant1Plant2Plant34021xx122021xx182321xxFormulatethemodelplantProductiontimeperbatch,hoursProductiontimeavailableperweek,hoursproduct1212310302241218Profitperbatch$3,000$5,0000,18231220401..53max2121212121xxxxxxxxtsxxzAnotherExample:RegionalPlanningTHESOUTHERCONFEDERATIONKIBBUTZIMisagroupofthreekibbutizm(communalfarmingcommunities)inIsrael.Thisofficeisplanningagriculturalproductionforthecomingyear.TheagricultureoutputofeachkibbutzislimitedbyboththeamountofavailableirrigablelandandthequantityofwaterallocatedforirrigationbytheWaterCommissioner.ThesedataaregiveninTable3.8.KibbutzUsableLand(Acres)WaterAllocation(AcreFeet)123400600300600800375Thecropssuitedforthisregionincludesugarbeets,cotton,andsorghum,andthesearethethreebeingconsideredfortheupcomingseason.Thesecropsdifferprimarilyintheirexpectednetreturnperacreandtheirconsumptionofwater.Inaddition,theMinistryofAgriculturehassetamaximumquotaforthetotalacreagethatcanbedevotedtoeachofthesecropsbytheSouthernConfederationofKibbutzim,asshowninTable3.9.cropMaximumquota(acres)Waterconsumption(acrefeet/acre)Netreturn($/acre)SugarbeetsCottonsorghum6005003253211,000750250Becauseofthelimitedwateravailableforirrigation,theSouthernConfederationofKibbutzimwillnotbeabletouseallitsirrigablelandforplanningcropsintheupcomingseason.Toensureequitybetweenthethreekibbutzim,ithasbeenagreedthateverykibbutzwillplantthesameproportionofitsavailableirrigableland.However,anycombinationofthecropsmaybegrownatanyofthekibbutzim.Thequestionis:Howmanyacrestodevotetoeachcropattherespectivekibbutzimwhilesatisfyingthegivenrestrictions.TheobjectiveistomaximizethetotalnetreturntothesouthernConfederationofKibbutzimasawhole.AnalyzeandformulatethemodelcropMaximumquota(acres)Waterconsumption(acrefeet/acre)Netreturn($/acre)SugarbeetsCottonSorghum6005003253211,000750250So,thedecisionvariablesareCropAllocationusablelandtoKibbutz123Sugarx11x12x13Cottonx21x22x23Sorghumx31x32x33TheobjectiveistomaximizetheNetReturn)(250)(750)(1000333231232221131211xxxxxxxxxMaxZTheconstraintsaremorecomplicated,wedividedthemintoafewkinds1.Usablelandforeachkibbutz:300600400333213322212312111xxxxxxxxx2.Waterallocationforeachkibbutz:375238002360023332313322212312111xxxxxxxxx3.Totalacreageforeachcrop:325500600333231232221131211xxxxxxxxx4.Equalproportionoflandplanted:400300300600600400312111332313332313322212322212312111xxxxxxxxxxxxxxxxxx5.Nonnegativity：9,,2,1,0jforxjSo,wecansee,anylinearprogrammingmodelinstituteofthreeparts:Decisionvariables,Objectivefunction,ConstraintsAndtoformulateamodeloflinearprogramminginstitutethreesteps(1)Determinedecisionvariables(2)Determ